Smart move looking to rent and not buy at this time. You'll have plenty to time to really get to know the area, which is impossible to do without spending lots of time here. If and when you decide to buy a few years down the road, you'll know for sure which towns you like and dislike, and if the whole Jersey thing is for you or not.
Not to mention, prices are falling around here; analysts predict home prices will be down 25% in 2009 alone, and who knows after that. It's a good time to save up your money!
I'm curious why you said you were looking for a place within reasonable commuting distance to NYC, but you haven't mentioned specifically you or your spouse working there. If you or your spouse commutes to NYC for work, then I would recommend looking at the area between New Brunswick and NYC, whereas Princeton is in the opposite direction. The commute from Princeton to NYC would be substantial, and could be a real drag.
Assuming that you really do need to commute to NYC, then you'll probably want to use public transportation so you should look at towns on the train line to NYC and within reasonable driving distance to New Brunswick, and that have some sort of downtown: Metuchen, Red Bank (nice downtown with added benefit of being closer to the shore), Westfield, Cranford, Maplewood, South Orange ... all of those towns come to mind, but others will probably have more suggestions.
If, however, you don't need to commute to NYC for work, and you threw it in there simply as a "nice to have" or as somewhere you might need to go once in a while but not every day, then you have a lot more options. You can avoid some of the train towns (which are more expensive) because you really don't need that on a daily basis and you're never far from a train station if you want to go into the city anyway, even if your town doesn't have one. Also, you can focus on areas in between New Brunswick and Princeton, because you don't have to worry about the commute to NYC. I'm less familiar with those areas, but I'm sure others will have some good suggestions for something south/west/southwest of New Brunswick.
Trying to find a "non-traumatizing" alternative to NYC is tricky if you consider New Brunswick to be too dangerous for your kids. There's always going to be slightly more crime in areas that are more urban and would give you a more "NYC-like" vibe. That said, I think kids are pretty adaptable and will adjust just fine wherever you end up; you'll probably be the one that has to make more of an adjustment.
I'd probably check out Red Bank and Metuchen first. I think Red Bank is bigger, so you might find more rental options there. Then check out Westfield and Cranford.
Good luck!